Initial program 59.6
\[-\frac{1}{\frac{\pi}{4}} \cdot \log \left(\frac{e^{\frac{\pi}{4} \cdot f} + e^{-\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{-\frac{\pi}{4} \cdot f}}\right)\]
Initial simplification59.6
\[\leadsto \log \left(\frac{e^{\frac{-\pi}{\frac{4}{f}}} + e^{\frac{\pi}{4} \cdot f}}{e^{\frac{\pi}{4} \cdot f} - e^{\frac{-\pi}{\frac{4}{f}}}}\right) \cdot \frac{-4}{\pi}\]
Taylor expanded around 0 0.8
\[\leadsto \log \left(\frac{e^{\frac{-\pi}{\frac{4}{f}}} + e^{\frac{\pi}{4} \cdot f}}{\color{blue}{\frac{1}{2} \cdot \left(f \cdot \pi\right) + \left(\frac{1}{192} \cdot \left({f}^{3} \cdot {\pi}^{3}\right) + \frac{1}{61440} \cdot \left({f}^{5} \cdot {\pi}^{5}\right)\right)}}\right) \cdot \frac{-4}{\pi}\]
Taylor expanded around 0 0.8
\[\leadsto \color{blue}{\left(4 \cdot \frac{\log f}{\pi} + \frac{7}{5760} \cdot \left({f}^{4} \cdot {\pi}^{3}\right)\right) - \left(4 \cdot \frac{\log \left(\frac{4}{\pi}\right)}{\pi} + \frac{1}{12} \cdot \left({f}^{2} \cdot \pi\right)\right)}\]
Simplified0.9
\[\leadsto \color{blue}{(\left(\frac{4}{\pi}\right) \cdot \left(\log f\right) + \left((\pi \cdot \left((\frac{7}{5760} \cdot \left(\left(\pi \cdot \pi\right) \cdot {f}^{4}\right) + \left(\frac{-1}{12} \cdot \left(f \cdot f\right)\right))_*\right) + \left(\left(-\frac{4}{\pi}\right) \cdot \log \left(\frac{4}{\pi}\right)\right))_*\right))_*}\]
- Using strategy
rm Applied add-cube-cbrt0.9
\[\leadsto (\left(\frac{4}{\pi}\right) \cdot \left(\log f\right) + \left((\pi \cdot \left((\frac{7}{5760} \cdot \left(\left(\pi \cdot \pi\right) \cdot {f}^{4}\right) + \left(\frac{-1}{12} \cdot \left(f \cdot f\right)\right))_*\right) + \left(\left(-\frac{4}{\pi}\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right) \cdot \sqrt[3]{\frac{4}{\pi}}\right)}\right))_*\right))_*\]
Applied log-prod0.9
\[\leadsto (\left(\frac{4}{\pi}\right) \cdot \left(\log f\right) + \left((\pi \cdot \left((\frac{7}{5760} \cdot \left(\left(\pi \cdot \pi\right) \cdot {f}^{4}\right) + \left(\frac{-1}{12} \cdot \left(f \cdot f\right)\right))_*\right) + \left(\left(-\frac{4}{\pi}\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right) + \log \left(\sqrt[3]{\frac{4}{\pi}}\right)\right)}\right))_*\right))_*\]
- Using strategy
rm Applied add-cube-cbrt0.9
\[\leadsto (\left(\frac{4}{\pi}\right) \cdot \left(\log f\right) + \left((\pi \cdot \left((\frac{7}{5760} \cdot \left(\left(\pi \cdot \pi\right) \cdot {f}^{4}\right) + \left(\frac{-1}{12} \cdot \left(f \cdot f\right)\right))_*\right) + \left(\left(-\frac{4}{\pi}\right) \cdot \left(\color{blue}{\left(\sqrt[3]{\log \left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right)} \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right)}\right) \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right)}} + \log \left(\sqrt[3]{\frac{4}{\pi}}\right)\right)\right))_*\right))_*\]
Final simplification0.9
\[\leadsto (\left(\frac{4}{\pi}\right) \cdot \left(\log f\right) + \left((\pi \cdot \left((\frac{7}{5760} \cdot \left({f}^{4} \cdot \left(\pi \cdot \pi\right)\right) + \left(\frac{-1}{12} \cdot \left(f \cdot f\right)\right))_*\right) + \left(\frac{-4}{\pi} \cdot \left(\log \left(\sqrt[3]{\frac{4}{\pi}}\right) + \left(\sqrt[3]{\log \left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right)} \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right)}\right) \cdot \sqrt[3]{\log \left(\sqrt[3]{\frac{4}{\pi}} \cdot \sqrt[3]{\frac{4}{\pi}}\right)}\right)\right))_*\right))_*\]
